Abstract: In this article we investigate maximal ideals in the lattice of all topologies on a fixed set. Padmanabhan and Rao were the first to study maximal ideals in this lattice. They characterized the principal maximal ideals. Their main result was incorrect but their approach proved helpful to us. We exhibit a class of nonprincipal maximal ideals and also give an example to show that the class in question is not exhaustive.